1908-9.] On Energy Accelerations and Partition of Energy. 359 
0 2 V „0 2 $, 
S]4>o 
dx 2 2 
dx-^ 2 
— = m i jh J ( sin 2 0 cos 2 sin 2 6 sin 2 <£ 4- cos 2 0 
dr 2 (mj + ro 2 ) 2 I S^ 2 fyj 2 V 
g2^ _ _ j 
4- terms of the type 2 h sin $ cos 0 sin > 
0 2 3v 
02<|» f 
m > 2 j sin 2 
? 'l + m 2) 2 * ^2 2 
+ terms which vanish when the mean values are taken J- 4- 
m 1>2 in2 e 2 ^ + ^ sin 2 e sin 2 ^ + — 2 C0S 2 0 
(>»! + m 2 ) 2 1 0*/ 02/ 2 2 3% 2 
d-f 
dr 
( 8V ] = m aVi J g in 2 ^ + CO g2 _ 2 sin <f> cos ^Y? 1 - 1 
r sin Od<j\r sin OdpJ (m l 4- m 2 ) 2 1 0x 1 2 dy^ dx-fiy^ J 
+ 
(m 1 4- ra 2 )- 
02<J> 02U> 
sin 2 ch — | + cos 2 <£- — | - 2 sin cos $ 
0.r 9 2 0i/ 9 2 
0^*i02/i 
0 2 <1>.> 
dx 2 dy 2 
} 
r 
+ 
thUll ) cos + sin 
sin 0(m 1 4- m 2 ) ( dx { dy 1 
d% 
d V2 
ixr,m, ( ,0$ o , . . 
— - — X - 2 - 1 - < cos <£— -? + sill 0 
r sin + m 2 ) ( cx 2 
Therefore 
Now, if sin 0 cos (p — l, sin 0 sin <p — m, and cos 0 = w, 
[£ 2 ] = [ai 2 ] = [ft 2 ] = ^-[^ 2 4- m 2 + ft 2 ] = -j . 
[sin 2 0 cos 2 <j>] = [sin 2 0 sin 2 <p] - [cos 2 0] = ^ . 
We obtain also the relations 
[sin 2 #] = -§-, [cos 2 6 cos 2 p] = J, [cos 2 0 sin 2 <£] = J , 
and 
[cos 2 </>] = [ sin 2 «/>] = J. 
If we take the mean values, we have, in accordance with our assumptions, 
0Y~ 
_ R/~ 
_0r _ 
Ldr_ 
_\dx 1 
+ y 2 z 
Y^k 2- 
\dx< 
+ 2/X|/X 9 
"03>i 0<h 2 
jdx^ dx 2 _ 
r/d/yn 
+ ™ 2 V i 2 
r pyi 
r ( 0 <i>2 Y 1 
2ft7 1 m 2 /x 1 /x 2 
\drj _ 
(nzj 4- w 2 ) 2 
_\0x 1 / 
(mj 4- m 2 ) 2 
_ \0fC 2 / _ 
(mj 4- m 9 ) 2 _ 
0$ x 0$,. 
dXn dx 
2-J 
2 m^fji^ 2 
r py! 
2m 2 [x 2 
r yyh 
4 m 1 m 2 fjL 1 ix 2 
0$! 0$ 2 
(m 1 + m 2 ) 2 
_ \0a; 1 / _ 
(m 1 + m 2 ) 2 
_\dx 2 J 
(m 1 + m 2 ) 2 
_0X 1 0d? 2 _ 
pi). 
r^ii 
r 0 2< h 9 i 
/X, 
i 
_0.r 1 2 _ 
4" /x 9 
2 
_dx 2 2 
02 Y~ 
d 2 f 
_j_ m 2 2 / X l 
_ 0 2 $ 1 
+ 
r0 2 $ 2 
07*2 _ 
[_dr 2 \ 
(to 2 4- m 2 ) 2 
0X X 2 _ 
(iftj 4- m 9 ) 2 
_0,r 2 2 _ 
0 2 Y 
_ m 2 Vi 
-02<|> i 
7?7i 2 /X 2 
rs^i 
0S 2 _ 
(Wj 4- m 2 ) 2 
_0X 1 2 _ 
(Wj + n? 9 ) 2 
— i 
Cl 
d 
CP | 
